MinT - Best Known (134−39, 134, s)-Nets in Base 8

Best Known (134−39, 134, s)-Nets in Base 8

(134−39, 134, 1026)-Net over F₈ — Constructive and digital

Digital (95, 134, 1026)-net over F₈, using

trace code for nets [i] based on digital (28, 67, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
    - the Hermitian function field over F₆₄ [i]

(134−39, 134, 3302)-Net over F₈ — Digital

Digital (95, 134, 3302)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−39, 134, 2375446)-Net in Base 8 — Upper bound on s

There is no (95, 134, 2375447)-net in base 8, because

1 times m-reduction [i] would yield (95, 133, 2375447)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 291131 233031 099946 274303 040104 379257 958928 798447 619375 633956 473560 170949 389646 007368 937301 678166 525678 801372 696332 695012 > 8¹³³ [i]