MinT - Best Known (186−61, 186, s)-Nets in Base 4

Best Known (186−61, 186, s)-Nets in Base 4

(186−61, 186, 240)-Net over F₄ — Constructive and digital

Digital (125, 186, 240)-net over F₄, using

trace code for nets [i] based on digital (1, 62, 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]

(186−61, 186, 549)-Net over F₄ — Digital

Digital (125, 186, 549)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−61, 186, 20694)-Net in Base 4 — Upper bound on s

There is no (125, 186, 20695)-net in base 4, because

1 times m-reduction [i] would yield (125, 185, 20695)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2406 294025 385157 810797 838411 685244 714887 581546 263309 646077 000231 755188 177018 464899 027458 568598 192335 954728 519400 > 4¹⁸⁵ [i]