MinT - Best Known (84−25, 84, s)-Nets in Base 4

Best Known (84−25, 84, s)-Nets in Base 4

(84−25, 84, 312)-Net over F₄ — Constructive and digital

Digital (59, 84, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 28, 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]

(84−25, 84, 430)-Net over F₄ — Digital

Digital (59, 84, 430)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84−25, 84, 25723)-Net in Base 4 — Upper bound on s

There is no (59, 84, 25724)-net in base 4, because

1 times m-reduction [i] would yield (59, 83, 25724)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 93 562995 054196 232525 728252 124825 118469 022632 208140 > 4⁸³ [i]