MinT - Best Known (107−34, 107, s)-Nets in Base 4

Best Known (107−34, 107, s)-Nets in Base 4

(107−34, 107, 240)-Net over F₄ — Constructive and digital

Digital (73, 107, 240)-net over F₄, using

1 times m-reduction [i] based on digital (73, 108, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 36, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(107−34, 107, 399)-Net over F₄ — Digital

Digital (73, 107, 399)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(107−34, 107, 14718)-Net in Base 4 — Upper bound on s

There is no (73, 107, 14719)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 26349 569282 293596 589394 830896 847488 751045 346290 008405 269298 107230 > 4¹⁰⁷ [i]