MinT - Best Known (45, 45+128, s)-Nets in Base 8

Best Known (45, 45+128, s)-Nets in Base 8

(45, 45+128, 98)-Net over F₈ — Constructive and digital

Digital (45, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 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]

(45, 45+128, 144)-Net over F₈ — Digital

Digital (45, 173, 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]

(45, 45+128, 933)-Net in Base 8 — Upper bound on s

There is no (45, 173, 934)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 797168 533515 225336 243426 922616 073579 051750 448054 810687 783492 071036 666501 072582 049636 553132 448666 982876 757632 168850 372686 136175 944431 411882 511365 064598 135086 > 8¹⁷³ [i]