MinT - Best Known (181−94, 181, s)-Nets in Base 4

Best Known (181−94, 181, s)-Nets in Base 4

(181−94, 181, 104)-Net over F₄ — Constructive and digital

Digital (87, 181, 104)-net over F₄, using

t-expansion [i] based on digital (73, 181, 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]

(181−94, 181, 129)-Net over F₄ — Digital

Digital (87, 181, 129)-net over F₄, using

t-expansion [i] based on digital (81, 181, 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]

(181−94, 181, 1236)-Net in Base 4 — Upper bound on s

There is no (87, 181, 1237)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 432157 553667 838029 780185 191263 326490 909763 455419 428555 198807 613744 152630 294955 626530 574342 909851 210935 314720 > 4¹⁸¹ [i]