MinT - Best Known (89, 89+32, s)-Nets in Base 8

Best Known (89, 89+32, s)-Nets in Base 8

(89, 89+32, 1026)-Net over F₈ — Constructive and digital

Digital (89, 121, 1026)-net over F₈, using

1 times m-reduction [i] based on digital (89, 122, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 61, 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]

(89, 89+32, 5957)-Net over F₈ — Digital

Digital (89, 121, 5957)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+32, 6562329)-Net in Base 8 — Upper bound on s

There is no (89, 121, 6562330)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18 788342 300343 912463 910164 161679 660324 362680 710180 772297 628783 097970 629817 973461 073557 289655 179795 034437 237247 > 8¹²¹ [i]