MinT - Best Known (63, 93, s)-Nets in Base 4

Best Known (63, 93, s)-Nets in Base 4

(63, 93, 240)-Net over F₄ — Constructive and digital

Digital (63, 93, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 31, 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]

(63, 93, 339)-Net over F₄ — Digital

Digital (63, 93, 339)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 93, 11560)-Net in Base 4 — Upper bound on s

There is no (63, 93, 11561)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 98 176101 852060 884613 814146 688098 046386 936575 020341 446560 > 4⁹³ [i]