MinT - Best Known (62−48, 62, s)-Nets in Base 81

Best Known (62−48, 62, s)-Nets in Base 81

(62−48, 62, 224)-Net over F₈₁ — Constructive and digital

Digital (14, 62, 224)-net over F₈₁, using

t-expansion [i] based on digital (13, 62, 224)-net over F₈₁, using
- net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
    - a function field by SÃ©mirat [i]

(62−48, 62, 298)-Net over F₈₁ — Digital

Digital (14, 62, 298)-net over F₈₁, using

t-expansion [i] based on digital (12, 62, 298)-net over F₈₁, using
- net from sequence [i] based on digital (12, 297)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 12 and N(F) ≥ 298, using
    - a curve from the manYPoints database [i]

(62−48, 62, 10424)-Net in Base 81 — Upper bound on s

There is no (14, 62, 10425)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 21235 772269 993764 044530 083900 153761 593904 622530 284262 476367 869370 013737 396874 418879 114968 383977 979193 125374 682880 176001 > 81⁶² [i]