MinT - Best Known (104−71, 104, s)-Nets in Base 4

Best Known (104−71, 104, s)-Nets in Base 4

(104−71, 104, 56)-Net over F₄ — Constructive and digital

Digital (33, 104, 56)-net over F₄, using

net from sequence [i] based on digital (33, 55)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
  - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(104−71, 104, 65)-Net over F₄ — Digital

Digital (33, 104, 65)-net over F₄, using

net from sequence [i] based on digital (33, 64)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 65, using
  - Drinfeld modules of rank 1 [i]

(104−71, 104, 246)-Net in Base 4 — Upper bound on s

There is no (33, 104, 247)-net in base 4, because

1 times m-reduction [i] would yield (33, 103, 247)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 109 200748 119008 428613 979393 623260 991792 534808 806969 608898 209216 > 4¹⁰³ [i]