MinT - Best Known (100, 100+44, s)-Nets in Base 8

Best Known (100, 100+44, s)-Nets in Base 8

(100, 100+44, 1026)-Net over F₈ — Constructive and digital

Digital (100, 144, 1026)-net over F₈, using

trace code for nets [i] based on digital (28, 72, 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]

(100, 100+44, 2572)-Net over F₈ — Digital

Digital (100, 144, 2572)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+44, 1054104)-Net in Base 8 — Upper bound on s

There is no (100, 144, 1054105)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11090 705163 249587 223128 739120 682318 040429 988174 049882 125997 204376 714542 376038 095435 218179 313394 404134 650576 998226 234093 338659 990196 > 8¹⁴⁴ [i]