MinT - Best Known (246−155, 246, s)-Nets in Base 4

Best Known (246−155, 246, s)-Nets in Base 4

(246−155, 246, 104)-Net over F₄ — Constructive and digital

Digital (91, 246, 104)-net over F₄, using

t-expansion [i] based on digital (73, 246, 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]

(246−155, 246, 144)-Net over F₄ — Digital

Digital (91, 246, 144)-net over F₄, using

net from sequence [i] based on digital (91, 143)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
  - Drinfeld modules of rank 1 [i]

(246−155, 246, 747)-Net in Base 4 — Upper bound on s

There is no (91, 246, 748)-net in base 4, because

1 times m-reduction [i] would yield (91, 245, 748)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3333 176702 102330 971643 565166 436910 803212 803344 217934 789747 159517 312638 506241 996941 202765 242965 368312 878065 940394 714629 510166 171187 842105 220025 899608 > 4²⁴⁵ [i]