MinT - Best Known (140−42, 140, s)-Nets in Base 8

Best Known (140−42, 140, s)-Nets in Base 8

(140−42, 140, 1026)-Net over F₈ — Constructive and digital

Digital (98, 140, 1026)-net over F₈, using

trace code for nets [i] based on digital (28, 70, 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]

(140−42, 140, 2816)-Net over F₈ — Digital

Digital (98, 140, 2816)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−42, 140, 1300139)-Net in Base 8 — Upper bound on s

There is no (98, 140, 1300140)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 707688 118186 663043 927107 757392 623276 207628 915516 941455 429909 436313 047885 320447 541434 112010 922817 273692 102391 742347 439237 751084 > 8¹⁴⁰ [i]