MinT - Best Known (70, 70+86, s)-Nets in Base 4

Best Known (70, 70+86, s)-Nets in Base 4

(70, 70+86, 66)-Net over F₄ — Constructive and digital

Digital (70, 156, 66)-net over F₄, using

t-expansion [i] based on digital (49, 156, 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]

(70, 70+86, 105)-Net over F₄ — Digital

Digital (70, 156, 105)-net over F₄, using

net from sequence [i] based on digital (70, 104)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 70 and N(F) ≥ 105, using
  - Drinfeld modules of rank 1 [i]

(70, 70+86, 825)-Net in Base 4 — Upper bound on s

There is no (70, 156, 826)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8622 574530 029725 964492 565098 596991 445980 019920 211459 200552 112723 362429 038880 823888 579600 949768 > 4¹⁵⁶ [i]