MinT - Best Known (160−97, 160, s)-Nets in Base 4

Best Known (160−97, 160, s)-Nets in Base 4

(160−97, 160, 66)-Net over F₄ — Constructive and digital

Digital (63, 160, 66)-net over F₄, using

t-expansion [i] based on digital (49, 160, 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]

(160−97, 160, 99)-Net over F₄ — Digital

Digital (63, 160, 99)-net over F₄, using

t-expansion [i] based on digital (61, 160, 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]

(160−97, 160, 578)-Net in Base 4 — Upper bound on s

There is no (63, 160, 579)-net in base 4, because

1 times m-reduction [i] would yield (63, 159, 579)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 576318 891038 142271 618016 799435 629583 766367 306919 617571 844076 111736 425451 625173 582257 748043 565596 > 4¹⁵⁹ [i]