MinT - Best Known (47, 47+19, s)-Nets in Base 4

Best Known (47, 47+19, s)-Nets in Base 4

(47, 47+19, 312)-Net over F₄ — Constructive and digital

Digital (47, 66, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 22, 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]

(47, 47+19, 415)-Net over F₄ — Digital

Digital (47, 66, 415)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+19, 30813)-Net in Base 4 — Upper bound on s

There is no (47, 66, 30814)-net in base 4, because

1 times m-reduction [i] would yield (47, 65, 30814)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1361 283903 778426 478673 815840 924031 744115 > 4⁶⁵ [i]