MinT - Best Known (83, 246, s)-Nets in Base 4

Best Known (83, 246, s)-Nets in Base 4

(83, 246, 104)-Net over F₄ — Constructive and digital

Digital (83, 246, 104)-net over F₄, using

t-expansion [i] based on digital (73, 246, 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, 246, 129)-Net over F₄ — Digital

Digital (83, 246, 129)-net over F₄, using

t-expansion [i] based on digital (81, 246, 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, 246, 619)-Net in Base 4 — Upper bound on s

There is no (83, 246, 620)-net in base 4, because

1 times m-reduction [i] would yield (83, 245, 620)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3589 720526 064366 990302 878467 240081 414754 776184 526598 593995 296777 011952 472673 093233 009360 716970 488478 845318 991375 105227 847236 310451 481250 341617 534158 > 4²⁴⁵ [i]