MinT - Best Known (76, 76+154, s)-Nets in Base 4

Best Known (76, 76+154, s)-Nets in Base 4

(76, 76+154, 104)-Net over F₄ — Constructive and digital

Digital (76, 230, 104)-net over F₄, using

t-expansion [i] based on digital (73, 230, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(76, 76+154, 112)-Net over F₄ — Digital

Digital (76, 230, 112)-net over F₄, using

t-expansion [i] based on digital (73, 230, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(76, 76+154, 556)-Net in Base 4 — Upper bound on s

There is no (76, 230, 557)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 150511 948387 458705 598874 864845 780521 544892 303352 904287 336934 795268 385719 119759 657714 955569 137891 504256 550332 014317 917157 132940 498044 682400 > 4²³⁰ [i]