MinT - Best Known (95, 95+161, s)-Nets in Base 4

Best Known (95, 95+161, s)-Nets in Base 4

(95, 95+161, 104)-Net over F₄ — Constructive and digital

Digital (95, 256, 104)-net over F₄, using

t-expansion [i] based on digital (73, 256, 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]

(95, 95+161, 144)-Net over F₄ — Digital

Digital (95, 256, 144)-net over F₄, using

t-expansion [i] based on digital (91, 256, 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]

(95, 95+161, 782)-Net in Base 4 — Upper bound on s

There is no (95, 256, 783)-net in base 4, because

1 times m-reduction [i] would yield (95, 255, 783)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3604 557041 289082 081113 404491 354299 877319 630275 185063 674290 130306 490304 235932 411261 500174 999400 440637 382205 975233 852593 652743 360915 160485 665164 601828 740656 > 4²⁵⁵ [i]