MinT - Best Known (159−36, 159, s)-Nets in Base 4

Best Known (159−36, 159, s)-Nets in Base 4

(159−36, 159, 1040)-Net over F₄ — Constructive and digital

Digital (123, 159, 1040)-net over F₄, using

1 times m-reduction [i] based on digital (123, 160, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 40, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(159−36, 159, 2536)-Net over F₄ — Digital

Digital (123, 159, 2536)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−36, 159, 523833)-Net in Base 4 — Upper bound on s

There is no (123, 159, 523834)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 534003 675939 329158 396509 440398 601170 471175 643761 076710 568556 093138 061716 629502 302522 748263 435196 > 4¹⁵⁹ [i]