MinT - Best Known (62, 62+111, s)-Nets in Base 8

Best Known (62, 62+111, s)-Nets in Base 8

(62, 62+111, 98)-Net over F₈ — Constructive and digital

Digital (62, 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]

(62, 62+111, 144)-Net over F₈ — Digital

Digital (62, 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]

(62, 62+111, 1998)-Net in Base 8 — Upper bound on s

There is no (62, 173, 1999)-net in base 8, because

1 times m-reduction [i] would yield (62, 172, 1999)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214893 617692 536412 900223 467795 213337 893921 266628 198910 301918 199909 107463 542264 192511 038905 259757 312497 480011 751141 446738 928073 319801 047271 339539 724938 028096 > 8¹⁷² [i]