MinT - Best Known (164−121, 164, s)-Nets in Base 8

Best Known (164−121, 164, s)-Nets in Base 8

(164−121, 164, 98)-Net over F₈ — Constructive and digital

Digital (43, 164, 98)-net over F₈, using

t-expansion [i] based on digital (37, 164, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(164−121, 164, 129)-Net over F₈ — Digital

Digital (43, 164, 129)-net over F₈, using

t-expansion [i] based on digital (38, 164, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(164−121, 164, 903)-Net in Base 8 — Upper bound on s

There is no (43, 164, 904)-net in base 8, because

1 times m-reduction [i] would yield (43, 163, 904)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1652 177933 189741 165527 252356 173198 368552 131119 114360 320859 206546 790320 485079 998122 002931 674802 407958 027691 891767 321739 908002 547738 112674 519573 145584 > 8¹⁶³ [i]