MinT - Best Known (150, 150+82, s)-Nets in Base 4

Best Known (150, 150+82, s)-Nets in Base 4

(150, 150+82, 163)-Net over F₄ — Constructive and digital

Digital (150, 232, 163)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (15, 56, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]
2. digital (94, 176, 130)-net over F₄, using
  - trace code for nets [i] based on digital (6, 88, 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]

(150, 150+82, 208)-Net in Base 4 — Constructive

(150, 232, 208)-net in base 4, using

2 times m-reduction [i] based on (150, 234, 208)-net in base 4, using
- trace code for nets [i] based on (33, 117, 104)-net in base 16, using
  - 3 times m-reduction [i] based on (33, 120, 104)-net in base 16, using
    - base change [i] based on digital (9, 96, 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]

(150, 150+82, 510)-Net over F₄ — Digital

Digital (150, 232, 510)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 150+82, 13693)-Net in Base 4 — Upper bound on s

There is no (150, 232, 13694)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 749326 951988 385041 538180 532086 511652 918379 805468 543779 385001 169730 022125 512239 847653 783141 099698 107799 011545 052539 141649 431301 299244 019475 > 4²³² [i]