MinT - Best Known (99, 99+43, s)-Nets in Base 8

Best Known (99, 99+43, s)-Nets in Base 8

(99, 99+43, 1026)-Net over F₈ — Constructive and digital

Digital (99, 142, 1026)-net over F₈, using

trace code for nets [i] based on digital (28, 71, 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]

(99, 99+43, 2688)-Net over F₈ — Digital

Digital (99, 142, 2688)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+43, 1435472)-Net in Base 8 — Upper bound on s

There is no (99, 142, 1435473)-net in base 8, because

1 times m-reduction [i] would yield (99, 141, 1435473)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 21 661728 841269 832499 639002 543113 359837 126161 380491 434101 888172 058759 200457 093303 796125 256262 736664 352844 592336 490525 944723 881792 > 8¹⁴¹ [i]