MinT - Best Known (78, 78+32, s)-Nets in Base 4

Best Known (78, 78+32, s)-Nets in Base 4

(78, 78+32, 312)-Net over F₄ — Constructive and digital

Digital (78, 110, 312)-net over F₄, using

t-expansion [i] based on digital (77, 110, 312)-net over F₄, using
- 1 times m-reduction [i] based on digital (77, 111, 312)-net over F₄, using
  - trace code for nets [i] based on digital (3, 37, 104)-net over F₆₄, using
    - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(78, 78+32, 582)-Net over F₄ — Digital

Digital (78, 110, 582)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+32, 31217)-Net in Base 4 — Upper bound on s

There is no (78, 110, 31218)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 685222 267643 872803 511161 607322 165686 724999 684096 035388 785461 499635 > 4¹¹⁰ [i]