MinT - Best Known (72, 72+88, s)-Nets in Base 4

Best Known (72, 72+88, s)-Nets in Base 4

(72, 72+88, 66)-Net over F₄ — Constructive and digital

Digital (72, 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]

(72, 72+88, 105)-Net over F₄ — Digital

Digital (72, 160, 105)-net over F₄, using

t-expansion [i] based on digital (70, 160, 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]

(72, 72+88, 853)-Net in Base 4 — Upper bound on s

There is no (72, 160, 854)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 155935 868189 902132 432994 738925 819224 636175 097697 868677 981425 457396 161264 267081 939230 922959 996956 > 4¹⁶⁰ [i]