MinT - Best Known (233−143, 233, s)-Nets in Base 4

Best Known (233−143, 233, s)-Nets in Base 4

(233−143, 233, 104)-Net over F₄ — Constructive and digital

Digital (90, 233, 104)-net over F₄, using

t-expansion [i] based on digital (73, 233, 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]

(233−143, 233, 129)-Net over F₄ — Digital

Digital (90, 233, 129)-net over F₄, using

t-expansion [i] based on digital (81, 233, 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]

(233−143, 233, 785)-Net in Base 4 — Upper bound on s

There is no (90, 233, 786)-net in base 4, because

1 times m-reduction [i] would yield (90, 232, 786)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48 493686 161849 758546 309474 089293 075074 711054 931794 519178 337526 457458 248759 497068 517103 914224 828504 964407 210250 256870 658311 645274 776893 518240 > 4²³² [i]