MinT - Best Known (164−125, 164, s)-Nets in Base 8

Best Known (164−125, 164, s)-Nets in Base 8

(164−125, 164, 98)-Net over F₈ — Constructive and digital

Digital (39, 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]

(164−125, 164, 129)-Net over F₈ — Digital

Digital (39, 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]

(164−125, 164, 770)-Net in Base 8 — Upper bound on s

There is no (39, 164, 771)-net in base 8, because

1 times m-reduction [i] would yield (39, 163, 771)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1649 161897 515956 676983 596676 060901 177658 814898 199157 008187 306572 352634 729811 038545 163510 169252 533915 410531 683308 233998 463943 975467 957842 201107 313216 > 8¹⁶³ [i]