MinT - Best Known (84, 84+40, s)-Nets in Base 4

Best Known (84, 84+40, s)-Nets in Base 4

(84, 84+40, 240)-Net over F₄ — Constructive and digital

Digital (84, 124, 240)-net over F₄, using

4¹ times duplication [i] based on digital (83, 123, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 41, 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]

(84, 84+40, 420)-Net over F₄ — Digital

Digital (84, 124, 420)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+40, 14944)-Net in Base 4 — Upper bound on s

There is no (84, 124, 14945)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 452 486657 252547 832126 686391 121729 596324 758539 877494 303585 556076 204260 396664 > 4¹²⁴ [i]