MinT - Best Known (80−35, 80, s)-Nets in Base 4

Best Known (80−35, 80, s)-Nets in Base 4

(80−35, 80, 98)-Net over F₄ — Constructive and digital

Digital (45, 80, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 40, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(80−35, 80, 103)-Net over F₄ — Digital

Digital (45, 80, 103)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−35, 80, 1488)-Net in Base 4 — Upper bound on s

There is no (45, 80, 1489)-net in base 4, because

1 times m-reduction [i] would yield (45, 79, 1489)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 368486 952240 085314 219509 755203 215447 533603 534420 > 4⁷⁹ [i]