MinT - Best Known (207−115, 207, s)-Nets in Base 4

Best Known (207−115, 207, s)-Nets in Base 4

(207−115, 207, 104)-Net over F₄ — Constructive and digital

Digital (92, 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]

(207−115, 207, 144)-Net over F₄ — Digital

Digital (92, 207, 144)-net over F₄, using

t-expansion [i] based on digital (91, 207, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(207−115, 207, 1057)-Net in Base 4 — Upper bound on s

There is no (92, 207, 1058)-net in base 4, because

1 times m-reduction [i] would yield (92, 206, 1058)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11042 273958 161917 015627 870021 978979 623476 024395 052272 945685 601398 863646 911317 645770 253635 405588 588914 917663 782431 563339 458688 > 4²⁰⁶ [i]