MinT - Best Known (186, 186+57, s)-Nets in Base 4

Best Known (186, 186+57, s)-Nets in Base 4

(186, 186+57, 1040)-Net over F₄ — Constructive and digital

Digital (186, 243, 1040)-net over F₄, using

1 times m-reduction [i] based on digital (186, 244, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 61, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(186, 186+57, 2993)-Net over F₄ — Digital

Digital (186, 243, 2993)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 186+57, 601708)-Net in Base 4 — Upper bound on s

There is no (186, 243, 601709)-net in base 4, because

1 times m-reduction [i] would yield (186, 242, 601709)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 950283 057432 026993 976439 914706 951091 776973 947635 070695 363607 093501 335958 028294 278837 136883 558821 037919 936377 661142 910919 277795 711627 042836 557966 > 4²⁴² [i]