MinT - Best Known (149−88, 149, s)-Nets in Base 4

Best Known (149−88, 149, s)-Nets in Base 4

(149−88, 149, 66)-Net over F₄ — Constructive and digital

Digital (61, 149, 66)-net over F₄, using

t-expansion [i] based on digital (49, 149, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(149−88, 149, 99)-Net over F₄ — Digital

Digital (61, 149, 99)-net over F₄, using

net from sequence [i] based on digital (61, 98)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 61 and N(F) ≥ 99, using
  - Drinfeld modules of rank 1 [i]

(149−88, 149, 593)-Net in Base 4 — Upper bound on s

There is no (61, 149, 594)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 526418 795658 482072 974531 616816 361854 583916 729596 496355 702736 517956 742030 362151 216200 122824 > 4¹⁴⁹ [i]