MinT - Best Known (131, 131+49, s)-Nets in Base 3

Best Known (131, 131+49, s)-Nets in Base 3

(131, 131+49, 288)-Net over F₃ — Constructive and digital

Digital (131, 180, 288)-net over F₃, using

trace code for nets [i] based on digital (11, 60, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(131, 131+49, 564)-Net over F₃ — Digital

Digital (131, 180, 564)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+49, 17712)-Net in Base 3 — Upper bound on s

There is no (131, 180, 17713)-net in base 3, because

1 times m-reduction [i] would yield (131, 179, 17713)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 25 400176 638703 432041 054661 178207 616224 112973 323793 233324 590108 844993 307160 885072 065761 > 3¹⁷⁹ [i]