MinT - Best Known (207−117, 207, s)-Nets in Base 4

Best Known (207−117, 207, s)-Nets in Base 4

(207−117, 207, 104)-Net over F₄ — Constructive and digital

Digital (90, 207, 104)-net over F₄, using

t-expansion [i] based on digital (73, 207, 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]

(207−117, 207, 129)-Net over F₄ — Digital

Digital (90, 207, 129)-net over F₄, using

t-expansion [i] based on digital (81, 207, 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]

(207−117, 207, 982)-Net in Base 4 — Upper bound on s

There is no (90, 207, 983)-net in base 4, because

1 times m-reduction [i] would yield (90, 206, 983)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11130 994500 268663 330339 192221 517454 889637 658088 084204 685429 598919 836806 157134 464979 368072 477652 803774 864196 725947 454637 522840 > 4²⁰⁶ [i]