MinT - Best Known (101, 101+43, s)-Nets in Base 8

Best Known (101, 101+43, s)-Nets in Base 8

(101, 101+43, 1026)-Net over F₈ — Constructive and digital

Digital (101, 144, 1026)-net over F₈, using

2 times m-reduction [i] based on digital (101, 146, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 73, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(101, 101+43, 2965)-Net over F₈ — Digital

Digital (101, 144, 2965)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(101, 101+43, 1749863)-Net in Base 8 — Upper bound on s

There is no (101, 144, 1749864)-net in base 8, because

1 times m-reduction [i] would yield (101, 143, 1749864)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1386 350073 436562 798737 574192 322641 925928 791703 215629 421320 408551 728757 475925 520613 016458 028287 364346 819843 122423 447608 939148 652286 > 8¹⁴³ [i]