MinT - Best Known (90, 90+115, s)-Nets in Base 4

Best Known (90, 90+115, s)-Nets in Base 4

(90, 90+115, 104)-Net over F₄ — Constructive and digital

Digital (90, 205, 104)-net over F₄, using

t-expansion [i] based on digital (73, 205, 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]

(90, 90+115, 129)-Net over F₄ — Digital

Digital (90, 205, 129)-net over F₄, using

t-expansion [i] based on digital (81, 205, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(90, 90+115, 1004)-Net in Base 4 — Upper bound on s

There is no (90, 205, 1005)-net in base 4, because

1 times m-reduction [i] would yield (90, 204, 1005)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 667 718104 486890 786470 473228 622099 237192 361847 464520 288730 118805 774918 910302 270476 313057 815625 929521 570479 150311 024107 691904 > 4²⁰⁴ [i]