MinT - Best Known (116, 116+60, s)-Nets in Base 4

Best Known (116, 116+60, s)-Nets in Base 4

(116, 116+60, 160)-Net over F₄ — Constructive and digital

Digital (116, 176, 160)-net over F₄, using

1 times m-reduction [i] based on digital (116, 177, 160)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 43, 30)-net over F₄, using
    - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
        F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. digital (73, 134, 130)-net over F₄, using
    - trace code for nets [i] based on digital (6, 67, 65)-net over F₁₆, using
      - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
        the Hermitian function field over F₁₆ [i]

(116, 116+60, 208)-Net in Base 4 — Constructive

(116, 176, 208)-net in base 4, using

2 times m-reduction [i] based on (116, 178, 208)-net in base 4, using
- trace code for nets [i] based on (27, 89, 104)-net in base 16, using
  - 1 times m-reduction [i] based on (27, 90, 104)-net in base 16, using
    - base change [i] based on digital (9, 72, 104)-net over F₃₂, using
      - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(116, 116+60, 454)-Net over F₄ — Digital

Digital (116, 176, 454)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+60, 13645)-Net in Base 4 — Upper bound on s

There is no (116, 176, 13646)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9193 766482 638817 592697 258120 739343 343798 269206 779283 469484 487300 095447 735520 493778 349872 888089 150881 030144 > 4¹⁷⁶ [i]