MinT - Best Known (128−79, 128, s)-Nets in Base 3

Best Known (128−79, 128, s)-Nets in Base 3

(128−79, 128, 48)-Net over F₃ — Constructive and digital

Digital (49, 128, 48)-net over F₃, using

t-expansion [i] based on digital (45, 128, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(128−79, 128, 64)-Net over F₃ — Digital

Digital (49, 128, 64)-net over F₃, using

net from sequence [i] based on digital (49, 63)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
  - a curve from the manYPoints database [i]

(128−79, 128, 239)-Net in Base 3 — Upper bound on s

There is no (49, 128, 240)-net in base 3, because

1 times m-reduction [i] would yield (49, 127, 240)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 484452 355556 969442 859013 330313 204164 158686 471491 201455 177537 > 3¹²⁷ [i]