MinT - Best Known (78, 78+37, s)-Nets in Base 4

Best Known (78, 78+37, s)-Nets in Base 4

(78, 78+37, 240)-Net over F₄ — Constructive and digital

Digital (78, 115, 240)-net over F₄, using

4¹ times duplication [i] based on digital (77, 114, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 38, 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]

(78, 78+37, 400)-Net over F₄ — Digital

Digital (78, 115, 400)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+37, 16355)-Net in Base 4 — Upper bound on s

There is no (78, 115, 16356)-net in base 4, because

1 times m-reduction [i] would yield (78, 114, 16356)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 431 473556 544171 427988 097703 616636 012046 012663 975579 153549 710250 731182 > 4¹¹⁴ [i]