MinT - Best Known (63, 154, s)-Nets in Base 8

Best Known (63, 154, s)-Nets in Base 8

(63, 154, 98)-Net over F₈ — Constructive and digital

Digital (63, 154, 98)-net over F₈, using

t-expansion [i] based on digital (37, 154, 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]

(63, 154, 144)-Net over F₈ — Digital

Digital (63, 154, 144)-net over F₈, using

t-expansion [i] based on digital (45, 154, 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]

(63, 154, 2933)-Net in Base 8 — Upper bound on s

There is no (63, 154, 2934)-net in base 8, because

1 times m-reduction [i] would yield (63, 153, 2934)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 496957 047697 594456 094272 121498 307618 734549 963655 012362 985289 568738 844035 427556 744179 784614 267293 460168 253585 950285 399668 878146 167567 799054 > 8¹⁵³ [i]