MinT - Best Known (60, 60+89, s)-Nets in Base 8

Best Known (60, 60+89, s)-Nets in Base 8

(60, 60+89, 98)-Net over F₈ — Constructive and digital

Digital (60, 149, 98)-net over F₈, using

t-expansion [i] based on digital (37, 149, 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]

(60, 60+89, 144)-Net over F₈ — Digital

Digital (60, 149, 144)-net over F₈, using

t-expansion [i] based on digital (45, 149, 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]

(60, 60+89, 2660)-Net in Base 8 — Upper bound on s

There is no (60, 149, 2661)-net in base 8, because

1 times m-reduction [i] would yield (60, 148, 2661)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 663395 347418 246380 513126 436628 666456 127999 536237 552343 571468 552518 335155 433948 197633 598340 647363 011201 658547 129470 291775 715339 988120 > 8¹⁴⁸ [i]