MinT - Best Known (52, 167, s)-Nets in Base 8

Best Known (52, 167, s)-Nets in Base 8

(52, 167, 98)-Net over F₈ — Constructive and digital

Digital (52, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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]

(52, 167, 144)-Net over F₈ — Digital

Digital (52, 167, 144)-net over F₈, using

t-expansion [i] based on digital (45, 167, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(52, 167, 1309)-Net in Base 8 — Upper bound on s

There is no (52, 167, 1310)-net in base 8, because

1 times m-reduction [i] would yield (52, 166, 1310)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 823552 057832 565729 455022 671363 441018 807492 246315 649927 462420 516932 614476 319955 109567 958874 974486 125799 983242 572093 893165 051462 520101 539106 346372 214280 > 8¹⁶⁶ [i]