MinT - Best Known (67, 67+106, s)-Nets in Base 8

Best Known (67, 67+106, s)-Nets in Base 8

(67, 67+106, 98)-Net over F₈ — Constructive and digital

Digital (67, 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]

(67, 67+106, 144)-Net over F₈ — Digital

Digital (67, 173, 144)-net over F₈, using

t-expansion [i] based on 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]

(67, 67+106, 2575)-Net in Base 8 — Upper bound on s

There is no (67, 173, 2576)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 723015 440590 751496 682311 784946 338479 310954 953112 033504 655766 506502 077673 245639 285054 004328 666960 781167 202637 376597 155180 827172 838564 040021 515291 474303 168224 > 8¹⁷³ [i]