MinT - Best Known (203−49, 203, s)-Nets in Base 4

Best Known (203−49, 203, s)-Nets in Base 4

(203−49, 203, 1032)-Net over F₄ — Constructive and digital

Digital (154, 203, 1032)-net over F₄, using

1 times m-reduction [i] based on digital (154, 204, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 51, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(203−49, 203, 2221)-Net over F₄ — Digital

Digital (154, 203, 2221)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−49, 203, 381555)-Net in Base 4 — Upper bound on s

There is no (154, 203, 381556)-net in base 4, because

1 times m-reduction [i] would yield (154, 202, 381556)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 317686 871872 246694 064339 359810 848980 153065 488666 130220 632800 201611 998773 008991 648092 004142 033390 161960 224020 097741 591764 > 4²⁰² [i]