MinT - Best Known (77, 77+65, s)-Nets in Base 8

Best Known (77, 77+65, s)-Nets in Base 8

(77, 77+65, 256)-Net over F₈ — Constructive and digital

Digital (77, 142, 256)-net over F₈, using

2 times m-reduction [i] based on digital (77, 144, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 72, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(77, 77+65, 336)-Net over F₈ — Digital

Digital (77, 142, 336)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+65, 17398)-Net in Base 8 — Upper bound on s

There is no (77, 142, 17399)-net in base 8, because

1 times m-reduction [i] would yield (77, 141, 17399)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 21 665058 981089 693578 718690 602076 416444 362720 997820 798932 179092 699427 817116 569707 899713 947255 445306 229402 682659 833560 884033 114541 > 8¹⁴¹ [i]