MinT - Best Known (64, 64+98, s)-Nets in Base 8

Best Known (64, 64+98, s)-Nets in Base 8

(64, 64+98, 98)-Net over F₈ — Constructive and digital

Digital (64, 162, 98)-net over F₈, using

t-expansion [i] based on digital (37, 162, 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]

(64, 64+98, 144)-Net over F₈ — Digital

Digital (64, 162, 144)-net over F₈, using

t-expansion [i] based on digital (45, 162, 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]

(64, 64+98, 2611)-Net in Base 8 — Upper bound on s

There is no (64, 162, 2612)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 203 036863 233130 927737 326455 686063 453916 375361 641310 219167 059069 179068 252730 507355 338297 788045 042209 663689 680126 312576 617380 522355 739174 044613 647093 > 8¹⁶² [i]