MinT - Best Known (91, 91+52, s)-Nets in Base 4

Best Known (91, 91+52, s)-Nets in Base 4

(91, 91+52, 139)-Net over F₄ — Constructive and digital

Digital (91, 143, 139)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (1, 27, 9)-net over F₄, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
      - the Hermitian function field over F₄ [i]
2. digital (64, 116, 130)-net over F₄, using
  - trace code for nets [i] based on digital (6, 58, 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]

(91, 91+52, 303)-Net over F₄ — Digital

Digital (91, 143, 303)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+52, 7181)-Net in Base 4 — Upper bound on s

There is no (91, 143, 7182)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 124 481883 648430 393275 920562 638751 931406 857831 331677 152044 816009 154058 806758 714188 769920 > 4¹⁴³ [i]