MinT - Best Known (77, 77+51, s)-Nets in Base 3

Best Known (77, 77+51, s)-Nets in Base 3

(77, 77+51, 128)-Net over F₃ — Constructive and digital

Digital (77, 128, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 64, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(77, 77+51, 130)-Net over F₃ — Digital

Digital (77, 128, 130)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+51, 1325)-Net in Base 3 — Upper bound on s

There is no (77, 128, 1326)-net in base 3, because

1 times m-reduction [i] would yield (77, 127, 1326)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 944476 507300 682011 525725 523109 834045 755511 575877 836421 372589 > 3¹²⁷ [i]