MinT - Best Known (155−93, 155, s)-Nets in Base 8

Best Known (155−93, 155, s)-Nets in Base 8

(155−93, 155, 98)-Net over F₈ — Constructive and digital

Digital (62, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 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]

(155−93, 155, 144)-Net over F₈ — Digital

Digital (62, 155, 144)-net over F₈, using

t-expansion [i] based on digital (45, 155, 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]

(155−93, 155, 2684)-Net in Base 8 — Upper bound on s

There is no (62, 155, 2685)-net in base 8, because

1 times m-reduction [i] would yield (62, 154, 2685)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 017788 270387 692003 647339 981543 993554 312020 607097 555260 364986 719240 901033 147834 055567 015422 641951 406475 178896 533703 106072 344145 309464 102104 > 8¹⁵⁴ [i]