MinT - Best Known (153−47, 153, s)-Nets in Base 3

Best Known (153−47, 153, s)-Nets in Base 3

(153−47, 153, 192)-Net over F₃ — Constructive and digital

Digital (106, 153, 192)-net over F₃, using

trace code for nets [i] based on digital (4, 51, 64)-net over F₂₇, using
- net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(153−47, 153, 327)-Net over F₃ — Digital

Digital (106, 153, 327)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(153−47, 153, 6685)-Net in Base 3 — Upper bound on s

There is no (106, 153, 6686)-net in base 3, because

1 times m-reduction [i] would yield (106, 152, 6686)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 338361 130230 554099 815277 157498 588986 429405 084223 784980 517469 954147 134233 > 3¹⁵² [i]