MinT - Best Known (80−45, 80, s)-Nets in Base 64

Best Known (80−45, 80, s)-Nets in Base 64

(80−45, 80, 513)-Net over F₆₄ — Constructive and digital

Digital (35, 80, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 80, 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]

(80−45, 80, 540)-Net over F₆₄ — Digital

Digital (35, 80, 540)-net over F₆₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−45, 80, 439875)-Net in Base 64 — Upper bound on s

There is no (35, 80, 439876)-net in base 64, because

1 times m-reduction [i] would yield (35, 79, 439876)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 48778 340705 312005 053303 789916 802557 843417 824779 669831 199314 523240 593513 185420 359279 786156 577286 787050 420082 504119 858435 931322 595722 417721 510896 > 64⁷⁹ [i]