MinT - Best Known (83, 83+126, s)-Nets in Base 4

Best Known (83, 83+126, s)-Nets in Base 4

(83, 83+126, 104)-Net over F₄ — Constructive and digital

Digital (83, 209, 104)-net over F₄, using

t-expansion [i] based on digital (73, 209, 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]

(83, 83+126, 129)-Net over F₄ — Digital

Digital (83, 209, 129)-net over F₄, using

t-expansion [i] based on digital (81, 209, 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]

(83, 83+126, 754)-Net in Base 4 — Upper bound on s

There is no (83, 209, 755)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 711819 031964 475465 374920 762145 795218 468965 768948 288485 094495 018168 022999 009957 758341 896509 707148 267457 319939 747604 550413 270016 > 4²⁰⁹ [i]