MinT - Best Known (89, 89+142, s)-Nets in Base 4

Best Known (89, 89+142, s)-Nets in Base 4

(89, 89+142, 104)-Net over F₄ — Constructive and digital

Digital (89, 231, 104)-net over F₄, using

t-expansion [i] based on digital (73, 231, 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]

(89, 89+142, 129)-Net over F₄ — Digital

Digital (89, 231, 129)-net over F₄, using

t-expansion [i] based on digital (81, 231, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(89, 89+142, 769)-Net in Base 4 — Upper bound on s

There is no (89, 231, 770)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 413292 906898 652393 154095 900271 140263 418210 915002 145675 359654 701336 268989 338817 132614 217543 889734 454262 223877 546674 700297 547017 750934 103424 > 4²³¹ [i]