MinT - Best Known (65, 65+31, s)-Nets in Base 4

Best Known (65, 65+31, s)-Nets in Base 4

(65, 65+31, 240)-Net over F₄ — Constructive and digital

Digital (65, 96, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 32, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(65, 65+31, 345)-Net over F₄ — Digital

Digital (65, 96, 345)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+31, 13909)-Net in Base 4 — Upper bound on s

There is no (65, 96, 13910)-net in base 4, because

1 times m-reduction [i] would yield (65, 95, 13910)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1569 790764 481742 761356 142771 639761 165657 508501 912184 201608 > 4⁹⁵ [i]