MinT - Best Known (130, 183, s)-Nets in Base 3

Best Known (130, 183, s)-Nets in Base 3

(130, 183, 252)-Net over F₃ — Constructive and digital

Digital (130, 183, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 61, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(130, 183, 461)-Net over F₃ — Digital

Digital (130, 183, 461)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 183, 11512)-Net in Base 3 — Upper bound on s

There is no (130, 183, 11513)-net in base 3, because

1 times m-reduction [i] would yield (130, 182, 11513)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 687 101734 567306 804560 034074 925636 924244 388787 350277 637454 098344 105262 799924 305425 256601 > 3¹⁸² [i]